Questions tagged [robust]
Robustness in general refers to a statistic's insensitivity to deviations from its underlying assumptions (Huber and Ronchetti, 2009).
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Examining country-level effects based on individual-level data combined with country-level data
I am new to working with country-level effects in comparative OLS regression with individual-level data. Are there any good resources for this?
Suppose my dependent variable is social integration (an ...
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Sum of Squares and partial $R^2$ in robust multiple regression
I would like to obtain estimates of the variance explained by each predictor in multiple regression using robust linear regression (for instance with the R function ...
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Solving Robust Regression for Weighted Least Squares
I hope that this message finds you well.
I am trying to solve a robust regression (Huber M-estimator) with iteratively reweighted least-squares by taking the following steps (as advised by the manual):...
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Entropy is the mean of -log(p). Is the mean all that's worth caring about?
Oftentimes, we try to maximize the expected reward. But generally, in control theory, you try to be risk-sensitive, and use more robust methods. For example, maximize the expected reward but give a ...
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Hypothesis testing for a weekly seasonal effect in the presence of outliers
Suppose that I have a time series where the mean usually changes smoothly over time, and I want a hypothesis test for whether there is a weekly seasonal pattern to the data. The time series also ...
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Does the presence of outliers always mean that robust regression analysis should be used?
I revised my question to be more specific, as suggested by the community. Since my knowledge of statistics is limited, I'm not entirely sure what it means to specialize in this subject—but I'll give ...
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Detecting Adversaries in Robust Mean Estimation Without Using Variance?
In robust mean estimation under strong contamination models (e.g., Huber's model or adversarial corruption), variance is often used to assign small weights to suspicious data sources Kane, D. M., ...
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Binary Multi-armed bandit with unbounded time varying choice independent noise
I have $k = |K|$ arms with unknown distribution $\nu_\alpha$ over $[0,1]$ and unknown mean $\mu_\alpha \in [0,1]$ where $\alpha \in K$.
The action $A_t \in \{1, \dots, K\}$ is chosen at time $t$ ...
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What is the difference between Theil-sen estimator and Repeated median regression?
I am currently learning about robust regression and came across two variants: the Theil–Sen estimator and Repeated Median Regression. However, I got confused when comparing these two algorithms. Both ...
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Robustness quantification of pass/failed experiment
I have the following table for two different methods tested in with two different conditions at a pass/failed task, e.g. $4/5$ means the method had succeeded 4 times out of 5 trials.
Condition 1
...
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Improving standard mean estimator for small samples
I have a series $X_1,\ldots X_n$ of iid random variables with finite expectation $\mu$, which is to be estimated. The standard estimator is $\frac{X_1+\ldots+X_n}{n}$, but I'd like to be protected ...
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How to calculate the slope of a line of best fit that minimizes mean absolute error?
I have 25 data points of the form $(x,y)$ where $x$ is $1,2,3,...,25$ and $y$ is the dependent variable.
I need to determine if $y$ values are increasing, decreasing, or staying the same.
The method ...
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Modelling a skewed response variable
I have a biomarker ratio (amyloid 42/40) and I am having issues modelling it. This is the proportion of a biomarker to another biomarker and it is important in diagnosing dementia. I am using as both ...
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Waldtest:Error in modelCompare(objects[[i - 1]], objects[[i]], vfun = vcov0) : nesting of models cannot be determined
I hope that someone can help me with the following problem with Waldtest and robustlmm package. I want to compare two robust regression models. I want to test ...
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Intercept significant, but confidence intervals around its standardized β include 0
I ran a HC (‘robust’) regression. The intercept is significant, which is reflected in the confidence intervals around the unstandardized betas. However, the CIs around the standardized β are quite ...
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What is the interpretation of outlier-robust principal component analysis?
There's a set of methods called "robust" principal component analysis (here, "robust" means resistant to influence from outliers). One example is Hubert et al., "ROBPCA: A new ...
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Improving Robustness of LSTM Model for Stock Price Prediction
I am currently working on a Long Short-Term Memory (LSTM) model for predicting stock prices. My model takes into account the fact that there are non-trading minutes with no data. I have also ...
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Binary response vs probability response
Consider these two scenarios:
respondents are asked to choose between two options offered to them (the resulting data is binary 0 & 1)
respondents are asked to give their probability of choice ...
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Robust estimation of standard deviation using relatively small sample taken from a Gaussian distribution
I'm sure this question was asked before, but I don't seem to be able to find a convincing answer.
If there is a relatively small set (say 3<n<20) of observations of a quantity that is assumed to ...
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ANOVA vs Kruskal Wallis - Small sample size
I have data from an experiment comparing plant weights for 4 independent treatment groups. The data seem to be normally distributed (I have been warned about using statistical tests for normality). ...
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Determine a robust trend from noisy time series data, when start and end years have a material effect
I have about 20 years of data, each year has a number of observations. If I put a linear trend through the data, I get a trend, and this trend differs based on the the choice of start and end year, ...
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Position M-estimators are affine equivariant (proof)
A position M-estimator of $\mu$ is defined as the solution of the equation (it is a $\mu$ such that):
$$\sum^{n}_{i=1} \psi\left(\frac{x_i - \mu}{ \sigma_0 } \right) = 0 $$
($\psi(x)$ is even and non-...
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Dummy regression group comparison
I want to do my ANCOVA as a robust regression as assumptions are hurt. I have a categorial predictor with 5 groups but I also want to check pairwaise for all groups if they differ in their effect on ...
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How to do an interaction in lmRob() function?
I am trying to compare 2 lmRob() models. One for male and one for female gender. Imagine my model like this:
...
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How to compare multiple linear regression statistically? [duplicate]
I am looking for a way to compare the results from two lmRob() functions statistically.
Here is an explanation what I am trying to do: My professor wants me to compare the results of two ancovas (one ...
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How can I compare the results of two lmRob() models? [closed]
I am looking for a way to compare the results from two lmRob() functions statistically.
Would that be a possible option for me:
lmrob_female <- robust::lmRob(Y ~ X_binary +
covariate1 + covariate2 +...
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Perturbation for more stable convex optimization
I am thinking of adding some perturbation to my convex optimization problem. The idea is straight forward like below chart. Supposed you are solving $\text{argmax} f(x) $, we want to find an $x$ that'...
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Sequential prediction/modeling without stationarity assumptions
Let's say that we have an arbitrary real-valued sequence of length $n$:
$$(x_{i})_{i \in \{0, \dots, n-1\}}.$$
If we wanted to try to create a probabilistic model for future values of the sequence ...
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How does Huber compute the $\operatorname{var}(s_n)/E[s_n]^2$ and $\operatorname{var}(d_n)/E[d_n]^2$?
(N.B. I am cross posting this question from math stackexchange since after
x days I have still not received any responses.)
How does Huber in book 'Robust statistical procedures' in chapter 1 compute ...
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How to implement an S-estimator
I'm trying to implement an MM-estimator in python. I have a working implementation of an M-estimator statsmodels.RLM - which is implemented as an iteratively re-weighted least squares algorithm. I am ...
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Effect of robust maximum likelihood estimator in structural equation modelling when data is normal?
I understand that when data are nonnormal robust maximum likelihood estimator can be used.
I'm wondering are there any disadvantages of using a robust maximum likelihood estimator when the data are ...
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Structural equation modeling (latent growth models): robust estimators to handle outliers?
Can I use robust estimators (e.g., "MLM" and "MLR"estimator lavaan options) to overcome outliers within my sample, or should I remove outliers?
For context, I am modelling the ...
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How are robust standard errors applied in logistic regression
I have been reading up on robust standard errors and had a few questions regarding how their use in logistic regression.
I have read here that heteroscedasticity is not an issue in logistic regression ...
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Robustness check in Structural Equation Modelling (SEM) in R
I have conducted SEM analysis in R and used Maximum Likelihood Robust estimator as my data are categorical and deviate from multivariate normality. when I submitted my manuscript, one reviewer asked ...
Bahar
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Influence function of the IQR
In class I am told the influence function of the IQR should be a constant times the difference between the influence function for the 75th percentile and the influence function for the 25th percentile,...
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Model comparsion for robust linear mixed models (robustlmm)
I'm currently working on a project where I've fitted 4 robust linear mixed models. However, I've hit a bit of a roadblock when it comes to model selection. I've been using the AIC (Akaike Information ...
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Anova violates normality assumption for error data
I have a 2 x 2 repeated measures ANOVA (N = 51) with Error Rate data as the dependent measure. The error data violates the normality assumption, even when outliers are removed. I have looked at the ...
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Robustness of Mann Whitney U Test for partially paired data
I'm curious if anyone is aware of a publication that addresses the following matter or could provide a mathematically or reasonable response to the following question:
In a pre-post study where ...
user392103
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Reconciling Nondeterministic and Probabilistic Decision Rules
I've been getting a bit stuck recently on how to reconcile the two seemingly-competing ideas of nondeterministic and probabilistic decision rules.
As an example:
Let $t=0$ denote the current time and ...
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Mediation model with non-normal data
I want to conduct a mediational analyses with three variables:
Predictor: it is the result of a memory test with range -1 to 1.
Mediator: it is the absolute error made by the participant when ...
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Is this algorithm for robust estimation of the covariance matrix sensible?
I have a high dimensional dataset $\bf{X} \subset \mathbb{R}^d$, which is multimodal and has outliers. I want to estimate a robust measure of association, something like the correlation between two ...
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Modeling outliers in maximum likelihood estimation with gradient descent
Consider a set of 3D points $X = \{x_1, x_2, ...x_n\} $ with $ x_i\in\mathbb{R}^3$ on which we want to fit an arbitrary probability distribution. The distribution we want to fit models some ...
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pros and cons of different robust measures of scale/ dispersion
I would very much appreciate some help regarding how to interpret different robust measures of scale (Inter-quartile range or IQR, biweight midvariance, and median absolute deviation or MAD). Thus, ...
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Is truncated mean a biased estimator
We have data $X_1, \dots, X_n$ which are i.i.d copies of $X$. Where we denote $\mathbb{E}[X] = \mu$, and $X$ has finite variance.
We define the truncated sample mean:
$\begin{align}
\hat{\mu}^{\...
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How to check for multicollinearity in Poisson regression model with robust error variance
I have created a Poisson regression model with robust error variance (https://academic.oup.com/aje/article/159/7/702/71883) to calculate relative risks.
This is the Poisson regression model:
...
Laura Omann
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Adjust the "Threshold" in a robust regression
I am trying to perform a robust regressions using the lmrob function in R.
I am getting this error Message:
...
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Robust regression (Passing-Pablok) with more than 50% of the points on the coordinate(0,0)
I have an issue with a regression problem. Indeed, I need to fit a linear regression on this data. The problem is more than 50% of the data points are located in the origin (0,0) of the graph (because ...
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Proving upper bound for truncated difference
Let $X$ and $Y$ be real valued random variables. And define a truncation operator as:
$\begin{align}
X(\tau) = (|X| \wedge \tau) \; \text{sign}(X), \quad \tau > 0
\end{align}$
Now, I am not ...
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Is Centering Data Around Their Medians in Least Absolute Deviation Regression Model (No Intercept), a Good Robust Practice For Smaller Data Sets?
Per the regression model:
$\mathbf{y} = f(\mathbf{x},\mathbf{\beta}) + \mathbf{\epsilon}$
Where the $\beta$ estimate of LAD regression is given by:
$ \hat{\beta}_{LAD} = \text{argmin}_{ b} \sum_{i=1}^...
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How to determine if my model is robust? Should the coefficients be same?
I want to run robustness tests for my model. For example, by reducing the sample to heavily concentrated groups, running a different regression (probit etc) etc. But, how do I ascertain that my ...
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